Question: Solve for $x$ and $y$ using elimination. ${3x+4y = 44}$ ${-3x-5y = -52}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. $-y = -8$ $\dfrac{-y}{{-1}} = \dfrac{-8}{{-1}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {3x+4y = 44}\thinspace$ to find $x$ ${3x + 4}{(8)}{= 44}$ $3x+32 = 44$ $3x+32{-32} = 44{-32}$ $3x = 12$ $\dfrac{3x}{{3}} = \dfrac{12}{{3}}$ ${x = 4}$ You can also plug ${y = 8}$ into $\thinspace {-3x-5y = -52}\thinspace$ and get the same answer for $x$ : ${-3x - 5}{(8)}{= -52}$ ${x = 4}$